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@article{748969, author = {Hilscher, Roman and Zeidan, Vera}, article_location = {San Diego (USA)}, article_number = {1}, keywords = {Time scale; Time scale symplectic system; Linear Hamiltonian system; Quadratic functional; Nonnegativity; Positivity; Conjoined}, language = {eng}, issn = {0022-247X}, journal = {Journal of Mathematical Analysis and Applications}, title = {Applications of time scale symplectic systems without normality}, volume = {340}, year = {2008} }
TY - JOUR ID - 748969 AU - Hilscher, Roman - Zeidan, Vera PY - 2008 TI - Applications of time scale symplectic systems without normality JF - Journal of Mathematical Analysis and Applications VL - 340 IS - 1 SP - 451-465 EP - 451-465 PB - Elsevier Science SN - 0022247X KW - Time scale KW - Time scale symplectic system KW - Linear Hamiltonian system KW - Quadratic functional KW - Nonnegativity KW - Positivity KW - Conjoined N2 - Recently, the authors obtained new characterizations of the positivity and nonnegativity of a time scale quadratic functional F with separable endpoints related to a time scale symplectic system (S). In these results, the assumption of normality is absent. In this paper we present applications of such results. Namely, without assuming normality we derive Sturmian comparison theorems, results for general jointly varying endpoints, and characterizations of the positivity of F via the corresponding time scale Riccati equation, a certain perturbed quadratic functional, and a time scale Riccati inequality. These results generalize and unify many recent as well as classical ones. ER -
HILSCHER, Roman a Vera ZEIDAN. Applications of time scale symplectic systems without normality. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Elsevier Science, 2008, roč.~340, č.~1, s.~451-465. ISSN~0022-247X.
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